Continuity mistake: Takumi and Shingo both have their right hands duct taped to the steering wheel, as per the rules of the Gum Tape Deathmatch. During one shot of the race, Tak's hand is no longer taped and resting casually on top of the steering wheel as opposed to the right side of it.
Continuity mistake: When Hayden starts doing his good luck routine, there is a football on the left side of the couch on a pillow. When he stands on the couch the ball rolls off the pillow. When he steps off the couch the ball is suddenly on the other side of the couch. The next shot the ball is back on the pillow.
Character mistake: Everyone is making a sincere effort to avoid touching the ball with their hands for the whole episode, even to the point of getting in late at school, but when the kids are waiting in line behind Ryo peeping into the classroom, a few of them have their hands on the ball. (00:06:45)